If the chicken is not sick, and you are just culling due to low egg production or pecking or some other non-illness issue - you can still use her meat. I am a chop the head off type of girl, so that is what we do here.
Older birds make fantastic stock and the meat can be used in soup or pot pies.
if the bird is sick or sucha thing you probably just want to dispose of the carcass (burial or trash) usually sick birds have so little on them that it isn't worth it o ryou have medicated or you just don't want to risk it...
dpends on the reason I am putting them down and the size of the bird...head chopping is always quick but it isn't always the quickest..if something really bad happens like the time I found a bird with a leg pulled off from a coon attack I go for faster means and wring their neck...not the swing them around thig bit a quick jerk snap thing
I either cut the neck and let them bleed out or do a cervical dislocation. For cervical dislocation you grab the head in one hand and give the body a hard flip downward to dislocate the neck or put the head under a broomstick, hold the broomstick in place with your feet, and pull on the legs until the dislocation occurs.
I prefer the knife or the broomstick. The body flip doesn't always give good results with lighter birds. The animal rights groups seem to prefer cervical dislocation as more humane than other methods.
I have never killed a chicken, having said that, when I was serving in the Army we used to kill Chickens and Rabbits on demonstration days. The qualified butcher would hold the chicken in one hand and with the other grab the chickens neck, twist and pull down. On many occaision the head would come away from the body. Appearently the most humane way to do it.
As long as the chicken is not got a disease of any kind then theres no reason why it can not be eaten.